Testing and characterizing the two-stage model of carcinogenesis for a wide range of human cancers

The age dependence of incidence for 45 cancer types in three populations is analyzed on a two-stage kinetic model containing three determinable parameters: (i) the fraction of population at risk for a cancer; (ii) the product of the frequencies of cancer-producing mutations, and (iii) the growth rate of the transformed clone from which a cancer ultimately evolves. The model, simplifying that proposed by others, fits many cancers. Data are easily handled in terms of the derived parameters, providing the basis for epidemiological analysis, here applied in detail to liver, cervix and testis cancers for nearly 50 world-wide populations. We identify 12 cancers for which only a limited fraction of the population is at risk. We argue that the appearance of most cancers requires at least three mutational events. For child, youth, or early adult cancers, one mutation may be congenital. We arrange the various cancers in a descending scale, defining six groups that differ in the derived mutation frequencies. A cancer appearing later in life, for which the whole population can be at risk, shows a low mutation frequency, consistent with background spontaneous mutation. The other cancers require increases in mutation frequency, arising from an increased rate of cell division and/or mutation rate.